size and value in china
TRANSCRIPT
Size and Value in China
by*
Jianan Liu, Robert F. Stambaugh, and Yu Yuan
First Draft: January 24, 2018
This version: August 27, 2018
Abstract
We construct size and value factors in China. The size factor excludes the smallest 30% offirms, which are companies valued significantly as potential shells in reverse mergers thatcircumvent tight IPO constraints. The value factor is based on the earnings-price ratio, whichsubsumes the book-to-market ratio in capturing all Chinese value effects. Our three-factormodel strongly dominates a model formed by just replicating the Fama and French (1993)procedure in China. Unlike that model, which leaves a 17% annual alpha on the earnings-price factor, our model explains most reported Chinese anomalies, including profitability andvolatility anomalies.
JEL classifications: G12, G14, G15Keywords: China, size, value, factors, anomalies
* We are grateful for comments from Jules van Binsbergen, Amir Yaron, seminar participants at the
Wharton School, conference participants at the 2018 Johns Hopkins Carey Finance Conference, and the
referee. We thank Danting Chang, Zhe Geng, and Wenhao Xun for excellent research assistance. Yuan
gratefully acknowledges financial support from the NSF of China (71522012). Author affiliations/contact
information:
Liu: The Wharton School, University of Pennsylvania, email: [email protected].
Stambaugh: The Wharton School, University of Pennsylvania and NBER, phone: 215-898-5734, email:
Yuan: Shanghai Mingshi Investment Co., Ltd, and Wharton Financial Institutions Center, University of
Pennsylvania, phone: +86-21-5010-6289, email: [email protected].
1. Introduction
China has the world’s second-largest stock market, helping to finance an economy that some
predict will be the world’s largest within a decade.1 China also has political and economic
environments quite different from those in the US and other developed economies. Moreover,
China’s market and investors are separated from the rest of the world. China largely prohibits
participation by foreign investors in its domestic stock market as well as participation by its
domestic investors in foreign markets.2
Factor models provide a cornerstone for investigating financial asset pricing and for de-
veloping investment strategies. Many studies of China’s stock market use a three-factor
model constructed by following the Fama and French (1993) procedure for US factors.3
The advisability of simply replicating a US model in China is questionable, however, given
China’s separation and the many differences in economic and financial systems. We explore
and develop factor models in China, allowing its unique environment to dictate alternative
approaches.
We start by examining size and value effects in the Chinese market. These two effects have
long been recognized elsewhere as important characteristics associated with expected return:
Banz (1981) reports a firm-size effect, and Basu (1983) finds an effect for the earnings-price
ratio, a popular value metric. Size and value are the most prominent characteristics used by
many institutions to classify investment styles. The most widely used non-market factors
in academic research are also size and value, following the influential study by Fama and
French (1993). Our study reveals that size and value effects are important in China, but
with properties different from the US. We construct size and value factors for China.
The size factor is intended to capture size-related differences in stock risk and return
that arise from size-related differences in the underlying businesses. In China, however,
the stock of a small listed firm is typically priced to reflect a substantial component of value
related not to the firm’s underlying business but instead to the Chinese initial public offering
1According to the World Bank, the 2016 equity values of listed domestic companies, in trillions of USdollars, are 27.4 in the US and 7.3 in China, followed by 5.0 in Japan. For a forecast that China’s GDPwill reach that of the US by 2028, see Bloomberg ( https://www.bloomberg.com/graphics/2016-us-vs-china-economy/).
2At the end of 2016, 197 foreign institutions were authorized to invest in A-shares, China’s domesticallytraded stocks, but with a quota of just 0.6% of total market value (and even less in earlier years). Chinesedomestic investors can invest in international financial markets only through a limited authorized channel.
3Examples of such studies include include Yang and Chen (2003), Fan and Shan (2004), Wang and Chin(2004), Chen, Kim, Yao, and Yu (2010), Cheung, Hoguet, and Ng (2015), and Hu, Chen, Shao, and Wang(2018).
1
(IPO) process. In China, the IPO market is strictly regulated, and a growing demand for
public listing confronts the low processing capacity of the regulatory bureau to approve
IPOs. As a consequence, private firms seek an alternative approach, a reverse merger, in
order to become public in a timely manner. In a reverse merger, a private firm targets a
publicly-traded company, a so-called “shell,” and gains control rights by acquiring its shares.
The shell then buys the private firm’s assets in exchange for newly issued shares. While
reverse mergers occur elsewhere, IPO constraints are sufficiently tight in China such that
the smallest firms on the major exchanges become attractive shell targets, unlike in the US,
for example.
The smallest listed firms are the most likely shells. In fact, 83% of the reverse mergers
in China involve shells coming from the smallest 30% of stocks. For a typical stock in the
bottom 30%, we estimate that roughly 30% of its market value reflects its potential shell
value in a reverse merger. Our estimate combines the empirical probability of being targeted
in a reverse merger with the average return accompanying that event. Consistent with the
contamination of small-firm stock prices by shell value, we also find that when compared to
other firms, the smallest 30% have returns less related to operating fundamentals, proxied
by earnings surprises, but more related to IPO activity. Therefore, to avoid shell-value
contamination when constructing any of our factors, we delete the bottom 30% of stocks,
which account for 7% of the stock market’s total capitalization.
The value effect in China is best captured by the earnings-price (EP ) ratio, versus other
valuation ratios. Following Fama and French (1992), we treat the choice among alternative
valuation ratios as an empirical question, asking which variable best captures the cross-
sectional variation in average stock returns. As in that study, we run a horserace among all
candidate valuation ratios, including EP , book-to-market (BM), asset-to-market, and cash-
to-price ratios. In a Fama-MacBeth regression including those four ratios, EP dominates
all others, just as Fama and French (1992) find BM dominates in the US market. Relying
on the latter US result, Fama and French (1993) use BM to construct their value factor.
Relying on our result for China, we use EP to construct our value factor.
Size and value are important factors in China, as revealed by their average premia as
well as their contributions to return variance. Our size and value factors both have average
premia exceeding 1% per month over our 2000–2016 sample period. For the typical stock in
China, size and value jointly explain an additional 15% of monthly return variance beyond
what the market factor explains. In comparison, size and value explain less than 10% of
additional return variance for the typical US stock during the same period.
2
Our three-factor model, CH-3, includes the market factor as well as size and value factors
incorporating the above China-specific elements. For comparison, we construct an alternative
three-factor model, FF-3, by simply replicating the Fama and French (1993) procedure. We
find that CH-3 strongly dominates FF-3. Specifically, FF-3 cannot price the CH-3 size and
value factors, which have (significant) FF-3 annualized alphas of 5.6% and 16.7%. In contrast,
CH-3 prices the FF-3 size and value factors, which have (insignificant) CH-3 annualized
alphas of just −0.5% and 4.1%. A Gibbons, Ross, and Shanken (1989) test of one model’s
ability to price the other’s factors gives a p-value of 0.41 for CH-3’s pricing ability but less
than 10−12 for FF-3’s ability.
We also investigate the ability of CH-3 to explain previously reported return anomalies
in China. A survey of the literature reveals anomalies in nine categories: size, value, prof-
itability, volatility, return-reversal, turnover, investment, accruals, and illiquidity. We find
each of the first six categories contains one or more anomalies that produce significant long-
short alphas with respect to the single-factor CAPM. CH-3 accommodates all anomalies in
the first four of those six categories, including profitability and volatility, whose anomalies
fail FF-3 explanations in the US. CH-3 fails only with some of the reversal and turnover
anomalies. In contrast, FF-3 leaves significant anomalies in five of the six categories. A total
of ten anomalies are unexplained by the CAPM; CH-3 explains eight of them, while FF-3
explains three. The average absolute CH-3 alpha for the ten anomalies is 5.4% annualized,
compared to 10.8% for FF-3 (average absolute t-statistics: 1.12 versus 2.70).
Hou, Xue, and Zhang (2015) and Fama and French (2015) add two factors based on
investment and profitability measures in their recently proposed factor models, Q-4 and FF-
5. Investment does not produce a significant CAPM alpha in China, and profitability is fully
explained by CH-3. In an analysis reported in the Appendix, we find that a replication of
FF-5 in China is dominated by CH-3.
Overall, CH-3 performs well as a factor model in China, and it captures most documented
anomalies. In US studies, researchers often supplement the usual three factors (market, size,
and value) with a fourth factor, such as the momentum factor of Carhart (1997) or the
liquidity factor of Pastor and Stambaugh (2003). We also add a fourth factor, motivated
by a phenomenon rather unique to China: a stock market dominated by individuals rather
than institutions. Over 101 million individuals have stock trading accounts in China, and
individuals own 88% of the market’s free-floating shares. This heavy presence of individuals
makes Chinese stocks especially susceptible to investor sentiment. To capture sentiment
effects, we base our fourth factor on turnover, which previous research identifies as a gauge
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of both market-wide and stock-specific investor sentiment (e.g. Baker and Stein, 2004,
Baker and Wurgler, 2006, and Lee, 2013). The resulting four-factor model, CH-4, explains
the turnover and reversal anomalies in addition to the anomalies explained by CH-3, thereby
handling all of China’s reported anomalies.
The remainder of the paper proceeds as follows. Section 2 discusses data sources and
sample construction. Section 3 addresses the interplay between firm size and China’s IPO
constraints and explores the importance of shell-value distortions in small-stock returns.
Section 4 investigates value effects in China. In Section 5, we construct CH-3 and FF-3
and compare their abilities to price each other’s factors. In Section 6, we compare the
abilities of those three-factor models to price anomalies. In Section 7, we construct CH-4 by
including a turnover factor and then analyze the model’s additional pricing abilities. Section
8 summarizes our conclusions.
2. Data source and samples
The data we use, which include data on returns, trading, financial statements, and mergers
and acquisitions, are from Wind Information Inc. (WIND), the largest and most prominent
financial data provider in China. WIND serves 90% of China’s financial institutions and
70% of the Qualified Foreign Institutional Investors (QFII) operating in China.
The period for our main analysis is from January 1, 2000 through December 31, 2016.
China’s domestic stock market, the A-share market, began in 1990 with the establishment
of the Shanghai and Shenzhen exchanges. We focus on the post-2000 period for two reasons.
The first is to assure uniformity in accounting data. The implementation of rules and
regulations governing various aspects of financial reporting in China did not largely take
shape until about 1999. Although 1993 saw the origination of principles for fair trade and
financial disclosure, firms received little guidance in meeting them. Companies took liberties
and imposed their own standards, limiting the comparability of accounting data across firms.
Not until 1998 and 1999 were laws and regulations governing trading and financial reporting
more thoroughly designed and implemented. For example, detailed guidelines for corporate
operating revenue disclosure were issued in December 1998 and implemented in January
1999. Securities laws were passed in December 1998 and implemented in July 1999. Only by
1999 did uniformity in accounting standards become widely accomplished. Because portfolios
formed in 2000 use accounting data for 1999, our post-2000 sample for portfolio returns relies
on accounting data more comparable across firms than in earlier years.
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The second reason for beginning our sample in 2000 is to ensure sufficient numbers of
observations. Portfolios are used in our study to construct factors and conduct many of the
tests. To enable reasonable precision and power, we require at least 50 stocks in all portfolios
after imposing our filters, which include eliminating stocks (i) in the bottom 30% of firm
size, (ii) listed less than six months, and (iii) having less than 120 trading records in the
past year or less than 15 trading records in the past month. This last pair of conditions
is intended to prevent our results from being influenced by returns that follow long trading
suspensions. Only by 1999 do the numbers of stocks in the market allow these criteria to be
met.
WIND’s data on reverse mergers begin in 2007, when the China Securities Regulatory
Commission identified the criteria of an M&A proposal that classify it as a reverse merger,
making such deals easier to trace. In Section 3.2, we use reverse merger data to estimate
shell values. Additional details about the data and the construction of empirical measures
are provided in the Appendix.
3. Small stocks and IPO constraints
Numerous studies in finance address China’s unique characteristics. For example, Allen,
Qian, and Qian (2003, 2005) compare China to other developed countries along various po-
litical, economic, and financial dimensions. Brunnermeier, Sockin, and Xiong (2017) study
China’s government interventions in its trading environment. Bian, Da, Lou, and Zhou
(2017) document the special nature of leveraged investors in China’s stock market. Song
and Xiong (2017) emphasize the necessity of accounting for the economy’s uniqueness when
analyzing risks in China’s financial system. Allen, Qian, Qian, and Zhao (2009) and Car-
penter and Whitelaw (2017) provide broader overviews of China’s financial environment.
One aspect of the Chinese market especially relevant for our study is the challenge faced
by firms wishing to become publicly traded. As discussed earlier, market values of the
smallest firms in China include a significant component reflecting the firms’ potential to be
shells in reverse mergers. Private firms often employ reverse mergers to become publicly
traded, rather than pursue the constrained IPO process. Subsection 3.1 describes that IPO
process, while subsection 3.2 describes reverse mergers and presents a notable example of
one in China. In subsection 3.3, we compute a simple estimate of the fraction of firm value
associated with being a shell for a potential reverse merger, and we find the fraction to be
substantial for the smallest stocks. Consistent with that result, we show in subsection 3.4
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that the returns on those stocks exhibit significantly less association with their underlying
firms’ fundamentals.
Our evidence demonstrating the importance of the shell component of small-firm values
is buttressed by contemporaneous research on this topic, conducted independently from ours.
In a study whose principal focus is the importance of shell values in China, Lee, Qu, and Shen
(2017) also show that the shell component is a substantial fraction of small-firm values and
that, as a result, the returns on small-firm stocks exhibit less sensitivity to fundamentals
but greater sensitivity to IPO activity. The Lee et al. (2017) study explores models for
pricing the shell-value firms, whereas we focus on models for pricing the “regular” stocks
constituting the other 93% of the stock market’s value.
3.1. The IPO process
In China, the IPO market is controlled by the China Securities Regulatory Commission
(CSRC). As a central planner, the CSRC constrains the IPO process to macro-manage the
total number of listed firms (e.g., Allen, Qian, Shan, and Zhao, 2014). Unlike the US, where
an IPO can clear regulatory scrutiny in a matter of weeks, undertaking an IPO in China is
long and tedious, easily taking three years and presenting an uncertain outcome. As detailed
in the Appendix, the process involves seven administrative steps, three bureau departments,
and a select 25-member committee that votes on each application. The committee meets
for both an initial review and a final vote, with those meetings separated by years. As of
November 2017, the CSRC reported 538 firms being processed, with just 31 having cleared
the initial review. The IPOs approved in early 2017 all entered the process in 2015.
The long waiting time can impose significant costs. During the review process, firms are
discouraged from any sort of expansion and must produce consistent quarterly earnings. Any
change in operations can induce additional scrutiny and further delay. A firm undertaking
an IPO may thus forgo substantial investment opportunities during the multi-year approval
process. Moreover, policy changes could prolong the process even more. In 2013, the CSRC
halted all reviews for nearly a year to cool down the secondary market.
3.2. Reverse mergers
Facing the lengthy IPO process, private firms wishing to become public often opt for an
alternative: reverse merger. A reverse merger, which is regulated as a merger and acquisition
(M&A), involves fewer administrative steps and is much faster. We illustrate the process via
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a real-life case involving the largest delivery company in China, SF Express (SF).
In 2016, SF decided to become public through a reverse merger. To be its shell firm,
SF targeted the small public company, DT Material (DT), with market value of about $380
million. SF and DT agreed on merger terms, and in May 2016 DT officially announced the
deal to its shareholders. At the same time, DT submitted a detailed M&A proposal to the
CSRC. The plan had DT issuing more than three billion shares to SF in exchange for all of
SF’s assets. The intent was clear: three billion shares would account for 97% of DT’s stock
upon the shares’ issuance. With those shares, SF would effectively be the sole owner of DT,
which would in turn be holding all of SF’s assets. DT would become essentially the same
old SF company but with publicly-traded status. The M&A authorization went smoothly.
By October 2016, five months after the application, the CSRC gave its conditional approval,
and final authorization came two months later. The merged company was trading as SF on
the Shenzhen Stock Exchange by February 2017. That same month, IPO applicants in the
2015 cohort had just begun their initial reviews.
The entire SF-DT process took less than a year, fairly typical for a reverse merger. The
greater speed of a reverse merger comes with a price tag, however. In addition to regular
investment banking and auditing fees, the private firm bears the cost of acquiring control of
the public shell firm. In the SF-DT case, DT kept 3% of the new public SF’s shares, worth
about $938 million. In the course of the deal, DT’s original shareholders made about 150%.
Reverse mergers also occur in the US. As in China, they have long been recognized
as an IPO alternative. From 2000 through 2008, the US averaged 148 reverse mergers
annually (Floros and Sapp, 2011). There is, however, a fundamental difference between
reverse mergers in the US versus China: Because IPOs are less constrained in the US, the
value of being a potential shell is much lower. In the US, the median shell’s equity market
value is only $2 million (Floros and Sapp, 2011), versus an average of $200 million in China.
Nearly all shell companies in the US have minimal operations and few non-cash assets. Their
Chinese counterparts are typically much more expensive operating businesses. As a result,
while small stocks on China’s major exchanges are attractive shell targets, small stocks on
the major US exchanges are not. Consistent with this difference, Floros and Sapp (2011)
observe that their US reverse-merger sample includes almost no shell targets listed on the
three major exchanges.
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3.3. Small stocks with large shell values
A private firm’s price tag for acquiring a reverse-merger shell depends essentially on the
shell’s market value. Not surprisingly, shells are most often small firms. Fig. 1 displays
the size distribution of public shells in our sample of reverse mergers covering the 2007–2016
period. Of the 133 reverse mergers, 83% come from the bottom 30%, and more than half come
from the bottom 10%. Given this evidence, we eliminate the bottom 30% when constructing
factors, to avoid much of the contamination of stock prices reflecting the potential to be
targeted as shells. Although the 30% cutoff is somewhat arbitrary, our results are robust to
using 25% and 35% as cutoffs.
What fraction of a firm’s market value owes to the firm potentially becoming a reverse-
merger shell? A back-of-the-envelope calculation suggests the fraction equals roughly 30%
for the stocks we eliminate (the bottom 30%). Let p denote the probability of such a stock
becoming a reverse-merger shell in any given period, and let G denote the stock’s gain in
value if it does become a shell. We can then compute the current value of this potential
lottery-like payoff on the stock as
S =pG+ (1− p)S
1 + r=
pG
r + p, (1)
where r is the discount rate. We take p to be the annual rate at which stocks in the bottom
30% become reverse-merger shells, and we take G to be the average accompanying increase
in stock value. Both quantities are estimated over a two-year rolling window. The annual
discount rate, r, is set to 3%, the average one-year deposit rate from 2007 to 2016.
Panel A of Fig. 2 plots the estimated daily ratio of shell value to market value, S/V ,
where V is the median market value of stocks in the bottom 30%. Over the 2009–2016
sample period, the average value of S/V is 29.5%, while the series fluctuates between 10%
and 60%. Equation (1) implicitly assumes the stock remains a potential shell in perpetuity,
until becoming a shell. In other words, the role of small stocks in reverse mergers is assumed
to be rather permanent in China, as the IPO regulatory environment shows no overall trend
toward loosening. Even if we reduce the horizon to 20 years, the average S/V remains about
half as large as the series plotted.
Panel B of Fig. 2 plots the estimated shell value, S, expressed in RMB. This value
exhibits a fivefold increase over the eight-year sample period, in comparison to barely a
twofold increase for the Shanghai-Shenzhen 300 index over the same period. The rise in S is
consistent with the significant premium earned over the period by stocks in the bottom 30%
of the size distribution. Recall, however, that these stocks account for just 7% of the stock
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market’s total capitalization. As we demonstrate later, constructing factors that include
these stocks, whose returns are distorted by the shell component, impairs the ability of those
factors to price the regular stocks that constitute the other 93% of stock-market value.
3.4. Return variation of small stocks
Given that the shell component contributes heavily to the market values and average
returns of the smallest stocks, we ask whether this component also contributes to variation
in their returns. If it does, then when compared to other stocks, returns on the smallest
stocks should be explained less by shocks to underlying fundamentals but more by shocks
to shell values. We explore both implications.
To compare responses to fundamentals, we analyze returns accompanying earnings an-
nouncements. We divide the entire stock universe into three groups, using the 30th and
70th size percentiles. Within each group, we estimate a panel regression of earnings-window
abnormal return on standardized unexpected earnings (SUE),
Ri,t−k,t+k = a+ b SUEi,t + ei,t, (2)
where earnings are announced on day t, and Ri,t−k,t+k is the cumulative return on stock i, in
excess of the market return, over the surrounding trading days from t− k through t+ k. We
compute SUEi,t using a seasonal random-walk, where SUEi,t = ∆i,t/σ(∆i), ∆i,t equals the
year-over-year change in stock i’s quarterly earnings, and σ(∆i) is the standard deviation of
∆i,t for the last eight quarters.
Under the hypothesis that the shell component is a significant source of return variation
for the smallest stocks, we expect those stocks to have a lower b in equation (2) and a lower
regression R2 than the other groups. The first three columns of Table 1 report the regression
results, which confirm our hypothesis. Panel A contains results for k = 0 in equation (2),
and Panel B has results for k = 3. In both panels, the smallest stocks have the lowest values
of b and R2. For comparison, we conduct the same analysis in the US and report the results
in the last three columns of Table 1. The US sample period is 1/1/1980–12/31/2016, before
which the quality of quarterly data is lower. In contrast to the results for China, the smallest
stocks in the US have the highest values of b and R2.
We also compare stocks’ return responses to shell-value shocks, using two proxies for
such shocks. One is the average return that public stocks experience upon becoming shells
in reverse mergers. Our rationale is that the higher is this return, the greater is the potential
value of becoming a shell. The other proxy is the log of the total number of IPOs, with the
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rationale that a greater frequency of IPOs could be interpreted by the market as a relaxing
of IPO constraints. Consistent with the importance of the shell component for the smallest
stocks, only that group’s returns covary both positively with the reverse-merger premium
and negatively with the log IPO number. The results are presented in the Appendix.
4. Value effects in China
A value effect is a relation between expected return and a valuation metric that scales the
firm’s equity price by an accounting-based fundamental. The long-standing intuition for
value effects (e.g., Basu, 1983, and Ball, 1992) is that a scaled price is essentially a catch-all
proxy for expected return: a higher (lower) expected return implies a lower (higher) current
price, other things equal.
Our approach to creating a value factor in China follows the same path established by the
two-study sequence of Fama and French (1992, 1993). Following Fama and French (1992),
the first step is to select the valuation ratio exhibiting the strongest value effect among a
set of candidate ratios. The valuation ratios Fama and French (1992) consider include EP ,
BM , and assets-to-market (AM). The authors find BM exhibits the strongest value effect,
subsuming the other candidates. Based on that result, the subsequent study by Fama and
French (1993) uses BM to construct the value factor (HML).
In this section we conduct the same horse race among valuation ratios. Our entrants are
the same as in Fama and French (1992), plus cash-flow-to-price (CP ). As in that study, we
estimate cross-sectional Fama and MacBeth (1973) regressions of individual monthly stock
returns on the valuation ratios, with a stock’s market capitalization and estimated CAPM
beta (β) included in the regression. For the latter variable we use the beta estimated from
the past year’s daily returns, applying a five-lag Dimson (1979) correction. Following Fama
and French (1992), we use EP to construct both EP+ and a dummy variable, where EP+
equals EP when EP is positive and zero otherwise, and the dummy variable, D(EP < 0),
equals one when EP is negative and zero otherwise. In the same manner, we construct CP+
and D(CP < 0) from CP . Due to the shell-value contamination of returns discussed earlier,
we exclude the smallest 30% of stocks.
Table 2 reports average slopes from the month-by-month Fama-MacBeth regressions.
Similar to results in the US market, we see from column (1) that β does not enter significantly.
Also as in the US, the size variable, log(ME), enters with a significantly negative coefficient
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that is insensitive to including β: in columns (2) and (3), without and with β beta included,
the size slopes are −0.0049 and −0.0046 with t-statistics of −2.91 and −2.69. These results
confirm a significant size effect in China.
Columns (4) through (7) of Table 2 report results when each valuation ratio is included
individually in its own regression. All four valuation ratios exhibit significant explanatory
power for returns. When the four valuation ratios are included in the regression simultane-
ously, as reported in column (8), EP dominates the others. The t-statistic for the coefficient
on EP+ is 4.38, while the t-statistics for logBM , logAM , and CP+ are just 1.31, 0.99, and
1.35. In fact, the coefficient and t-statistic for EP+ in column (8) are very similar to those
in column (6), where EP is the only valuation ratio in the regression. The estimated EP
effect in column (8) is also economically significant. A one-standard-deviation difference in
EP+ implies a difference in expected monthly return of 0.52%.
Because BM likely enters the horse race as a favorite, we also report in column (9)
the results when BM and EP are the only valuation ratios included. The results are very
similar, with the coefficient and t-statistic for EP+ quite close to those in column (8), and
with the coefficient on logBM only marginally significant.
Fama and French (1992) exclude financial firms, whereas we include them in Table 2. We
do so because we also include financial firms when constructing our factors, as do Fama and
French (1993) when constructing their factors. If we instead omit financial firms (including
real estate firms) when constructing Table 2, the results (reported in the Appendix) are
virtually unchanged.
In sum, we see that EP emerges as the most effective valuation ratio, subsuming the
other candidates in a head-to-head contest. Therefore, in the next section we construct our
value factor for China using EP . The dominance of EP over BM is further demonstrated in
the next section, where we show that our CH-3 model with the EP -based value factor prices
a BM -based value factor, whereas the BM -based model, FF-3, cannot price the EP -based
value factor.
5. A three-factor model in China
In this section we present our three-factor model, CH-3, with factors for size, value, and
the market. Our approach incorporates the features of size and value in China discussed
in the previous sections. Subsection 5.1 provides details of the factor construction. We
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then compare our approach to one that ignores the China-specific insights. Subsection 5.2
illustrates the problems with including the smallest 30% of stocks, while subsection 5.3 shows
that using EP to construct the value factor dominates using BM .
5.1. Size and value factors
Our model has two distinct features tailored to China. First, we eliminate the smallest
30% of stocks, to avoid their shell-value contamination, and we use the remaining stocks
to form factors. Second, we construct our value factor based on EP . Otherwise, we follow
the procedure used by Fama and French (1993). Specifically, each month we separate the
remaining 70% of stocks into two size groups (Small and Big), split at the median market
value of that universe. We also break that universe into three EP groups: top 30% (Value),
middle 40%(Middle), and bottom 30%(Growth). We then use the intersections of those
groups to form value-weighted portfolios for the six resulting size-EP combinations: S/V,
S/M, S/G, B/V, B/M, and B/G. Our size and value factors, denoted as SMB (Small-
minus-Big) and VMG (Value-minus-Growth), combine the returns on these six portfolios as
follows:
SMB =1
3(S/V + S/M + S/G)− 1
3(B/V +B/M +B/G),
V MG =1
2(S/V +B/V )− 1
2(S/G+B/G).
The market factor, MKT , is the return on the value-weighted portfolio of our universe, the
top 70% of stocks, in excess of the one-year deposit interest rate.
Table 3 reports summary statistics for the three factors in our 204-month sample period.
The monthly standard deviations of SMB and VMG are 4.52% and 3.75%, each roughly
half of the market’s standard deviation of 8.09%. The averages of SMB and VMG are
1.03% and 1.14% per month, with t-statistics of 3.25 and 4.34. In contrast, the market
factor has a 0.66% mean with a t-statistic of just 1.16. Clearly, size and value command
substantial premiums in China over our sample period. All three factors are important for
pricing, however, in that each factor has a significantly positive alpha with respect to the
other two factors. Specifically, those two-factor alphas for MKT , SMB, and VMG are
1.57%, 1.91%, and 1.71%, with t-statistics of 2.30, 6.92, and 7.94. Each factor’s two-factor
alpha exceeds its corresponding simple average essentially due to the negative correlations
of VMG with both MKT and SMB (−0.27 and −0.62). In China, smaller stocks tend to
be growth stocks, making the negative correlation between size and value stronger than it is
in the US. Fama-Macbeth regressions also reveal a substantial negative correlation between
China’s size and value premia. For example, the correlation between the coefficients on
12
logME and EP+ underlying the results reported in column (6) of Table 2 equals 0.42. Note
that a positive correlation there is consistent with a negative correlation between the premia
on (small) size and value.
As Ross (2017) argues, explaining average return is one of two desiderata for a parsimo-
nious factor model. Explaining return variance is the other. Table 4 reports the average
R-squared values in regressions of individual stock returns on one or more of the CH-3 fac-
tors. Panel A includes all listed stocks in China, while Panel B omits the smallest 30%.
For comparison with the US, over the same period from January 2000 through December
2016, Panel C reports results when regressing NYSE/Amex/Nasdaq stocks on one or more of
the three factors of Fama and French (1993). All regressions are run over rolling three-year
windows, and the R-squared values then averaged over time and across stocks.
We see from Table 4 that our size and value factors explain substantial fractions of return
variance beyond what the market factor explains. Across all Chinese stocks, for example,
the three CH-3 factors jointly explain 53.6% of the typical stock’s return variance, versus
38.5% explained by just the market factor. The difference between these values, 15.1%, is
actually higher than the corresponding 9.6% difference for the US (27.3% minus 17.7%). Size
and value individually explain substantial additional variance, again with each adding more
R-squared in China than in the US. We also see that the explanatory power of the CH-3
factors, which are constructed using the largest 70% of stocks, improves when averaging just
over that universe (Panel B versus Panel A). The improvement is rather modest, however,
indicating that our factors explain substantial variance even for the shell stocks.
A striking China-US difference is that the market factor in China explains more than
twice as large a fraction of the typical stock’s variance than the market factor explains in
the US: 38.5% versus 17.7%. The high average R-squared in China is more typical of earlier
decades in US history. For example, Campbell, Lettau, Malkiel, and Xu (2001) report
average R-squared values exceeding 30% in the US during the 1960s. Exploring potential
sources of the higher explanatory power of the market factor in China seems an interesting
direction for future research.
Naturally, diversification allows the CH-3 factors to explain larger fractions of return
variance for portfolios than for individual stocks. For example, we form value-weighted
portfolios within each of 37 industries, using classifications provided by Shenyin-Wanguo
Security Co., the leading source of industry classifications in China. On average across
industries, the CH-3 factors explain 82% of the variance of an industry’s return, versus 72%
explained by the market factor. For the anomalies analyzed later, the CH-3 factors typically
13
explain 90% of the return variance for a portfolio formed within a decile of an anomaly
ranking variable, versus 85% explained by the market.
We keep negative EP stocks in our sample and categorize them as growth stocks, ob-
serving that negative-EP stocks comove with growth stocks. Returns on the negative EP
stocks load negatively on a value factor constructed using just the positive-EP sample, with
a slope coefficient of −0.28 and a t-statistic of −3.31. As a robustness check, we exclude
negative EP stocks and find all our results hold. On average across months, negative-EP
stocks account for 15% of the stocks in our universe.
In sum, size and value, as captured by our model’s SMB and VMG, are important
factors in China. This conclusion is supported by the factors’ average premia as well as their
ability to explain return variances.
5.2. Including shell stocks
If we construct our three factors without eliminating the smallest 30% of stocks, the
monthly size premium increases to 1.36% while the value premium shrinks to 0.87%. As
observed earlier, the value of being a potential reverse-merger shell has grown significantly
over time, creating a shell premium that accounts for a substantial portion of the smallest
stocks’ average returns. Consequently, a size premium that includes shell stocks is distorted
upward by the shell premium. At the same time, the shell premium distorts the value
premium downward. Market values of small firms with persistently poor or negative earnings
nevertheless include significant shell value, so those firms’ resulting low EP ratios classify
them as growth firms. Misidentifying shell firms as growth firms then understates the value
premium due to the shell premium in returns on those “growth” firms.
High realized returns on shell stocks during our sample period should not necessarily be
interpreted as evidence of high expected returns. The high returns could reflect unanticipated
increases in rationally priced shells, or they could reflect overpricing of shells in the later
years (implying low expected subsequent returns). With rational pricing, an increase in shell
value could either raise or lower expected return on the shell firms’ stocks, depending on the
extent to which shell values contain systematic risks. We do not attempt to explain expected
returns on shell stocks. Lee et al. (2017) link expected returns on these stocks to systematic
risk related to regulatory shocks.
Including shell stocks also impairs the resulting factor model’s explanatory power. When
the three factors include the bottom 30% of stocks, they fail to price SMB and VMG from
14
CH-3, which excludes shells: shell-free SMB produces an alpha of −23 basis points (bps) per
month (t-statistic: −3.30), and VMG produces an alpha of 27 bps (t-statistic: 3.32). These
results further confirm that the smallest 30% of stocks are rather different animals. Although
they account for just 7% of the market’s total capitalization, including them significantly
distorts the size and value premia and impairs the resulting model’s explanatory ability.
Therefore, excluding shells is important if the goal is to build a model that prices regular
stocks.
5.3. Comparing size and value factors
The obvious contender to CH-3 is FF-3, which follows Fama and French (1993) in using
BM instead of EP as the value metric. In this subsection, we compare CH-3 to FF-3,
asking whether one model’s factors can explain the other’s. Using the same stock universe
as CH-3, we construct the FF-3 model’s size and value factors, combining the six size-BM
value-weighted portfolios (S/H, S/M, S/L, B/H, B/M, B/L). The size groups are again split
at the median market value, and the three BM groups are the top 30% (H), middle 40%
(M), and bottom 30% (L). The returns on the resulting six portfolios are combined to form
the FF-3 size and value factors as follows:
FFSMB =1
3(S/H + S/M + S/L)− 1
3(B/H +B/M +B/L),
FFHML =1
2(S/H +B/H)− 1
2(S/L+B/L).
The market factor is the same as in the CH-3 model.
Our CH-3 model outperforms FF-3 in China by a large margin. Panel A of Table 5
reports the alphas and corresponding t-statistics of each model’s size and value factors with
respect to the other model. CH-3 prices the FF-3 size and value factors quite well. The CH-3
alpha of FFSMB is just −4 bps per month, with a t-statistic of −0.66, while the alpha of
FFHML is 34 bps, with a t-statistic of 0.97. In contrast, FF-3 prices neither the size nor
the value factor of CH-3. FF-3 removes less than half of our model’s 103 bps size premium,
leaving an SMB alpha of 47 bps with a t-statistic of 7.03. Most strikingly, the alpha of our
value factor, VMG, is 139 bps per month (16.68% annually), with a t-statistic of 7.93.
Panel B of Table 5 reports GRS tests of whether both of a model’s size and value factors
jointly have zero alphas with respect to the other model. The results tell a similar story as
above. The test of zero CH-3 alphas for both FFSMB and FFHML fails to reject that
null, with a p-value of 0.41. In contrast, the test strongly rejects jointly zero FF-3 alphas for
15
SMB and VMG, with a p-value less than 10−12. The Appendix reports additional details
of the regressions underlying the results in Table 5.
The above analysis takes a frequentist approach in comparing the abilities of models to
explain each other’s factors. Another approach to making this model comparison is Bayesian,
proposed by Barillas and Shanken (2018) and also applied by Stambaugh and Yuan (2017).
This approach compares factor models in terms of posterior model probabilities across a
range of prior distributions. Consistent with the above results, this Bayesian comparison
of FF-3 to CH-3 also heavily favors the latter. Details of the analysis are presented in the
Appendix.
In the US, two additional factors, profitability and investment, appear in recently pro-
posed models by Hou et al. (2015) and Fama and French (2015). Guo, Zhang, Zhang,
and Zhang (2017) construct the Fama-French five-factor model in China (FF-5) and find
that, when benchmarked against the CAPM, the investment factor is very weak while the
profitability factor is significant. We also find that the investment effect is weak in China,
yielding no significant excess return spread or CAPM alpha. A profitability spread has a
significant CAPM alpha but does not survive CH-3. Accordingly, in the same tests as above,
CH-3 again dominates. The CH-3 alphas for the non-market factors in FF-5 produce a GRS
p-value of 0.88, whereas the FF-5 alphas for the SMB and VMG factors of CH-3 produce
a GRS p-value of 0.0003. Details are presented in the Appendix.
6. Anomalies and factors
A factor model is often judged by its ability not only to price another model’s factors but
also to explain return anomalies. In this section we explore the latter ability for CH-3 versus
FF-3. We start by compiling a set of anomalies in China that are reported in the literature.
For each of those anomalies, we compute a long-short return spread in our sample, and we
find ten anomalies that produce significant alphas with respect to a CAPM benchmark. Our
CH-3 model explains eight of the ten, while FF-3 explains three.
6.1. Anomalies in China
Our survey of the literature reveals 14 anomalies reported for China. The anomalies
fall into nine categories: size, value, profitability, volatility, reversal, turnover, investment,
accruals, and illiquidity. The literature documenting Chinese anomalies is rather heteroge-
16
neous with respect to sample periods, data sources, and choice of benchmarking model (e.g.,
one factor, three factors, or no factors). Our first step is to re-examine all of the anomalies
using our data and sample period. As discussed earlier, our reliance on post-2000 data and
our choice of WIND as the data provider offer the most reliable inferences. We also use one
model, the CAPM, to classify all the anomalies as being significant or not. Unlike the previ-
ous literature, we also evaluate the anomalies within our stock universe that eliminates the
smallest 30%, so that shell values do not contaminate anomaly effects. For the 14 anomalies
we find in the literature, the Appendix reports their CAPM alphas as well as the conclusions
of each previous study examining one or more of the anomalies.
For our later analysis of the pricing abilities of the three-factor models, we retain only the
anomalies that generate significant CAPM alphas for long-short spreads between portfolios
of stocks in the extreme deciles. This non-parametric approach of comparing the extreme
deciles, as is common in the anomalies literature, is robust to any monotonic relation but
relies on having a sufficiently large sample to achieve power. After imposing our filters, the
number of stocks grows from 610 in 2000 to 1872 in 2016, so each portfolio contains at least
60 stocks even early in the sample period. Nevertheless, our 17-year period is somewhat
shorter than is typical of US studies, so any of our statements about statistical insignificance
of an anomaly must be tempered by this power consideration.
We compute alphas for both unconditional and size-neutral sorts. We conduct the latter
sort because correlation between an anomaly variable and size could obscure an anomaly’s
effect in an unconditional sort, given China’s large size premium of 12.36% annually. For each
of the 14 anomalies, the two sorting methods are implemented as follows: The unconditional
sort forms deciles by sorting on the anomaly variable. (For EP and CP, we sort only the
positive values.) We then construct a long-short strategy using deciles one and ten, forming
value-weighted portfolios within each decile. The long leg is the higher-performing one, as
reported by previous studies and confirmed in our sample. For the size-neutral version, we
first form size deciles by sorting on the previous month’s market value. Within each size
decile, we then create ten deciles formed by sorting on the anomaly variable. Finally, we form
the anomaly decile portfolios used in our tests. We pool all stocks that fall within a given
anomaly decile for any size decile. The returns on those stocks are then value-weighted, using
the individual stocks’ market capitalizations, to form the portfolio return for that anomaly
decile. As with the unconditional sort, the long-short strategy again uses deciles one and
ten.
Our procedure reveals significant anomalies in six categories: size, value, profitability,
17
volatility, reversal, and turnover. Almost all of the anomalies in these categories produce
significant CAPM-adjusted return spreads from both unconditional and size-neutral sorts.
Although the investment, accrual, and illiquidity anomalies produce significant CAPM alphas
in the US, they do not in China, for either unconditional or size-neutral sorts. The estimated
monthly alphas for investment are small, at 0.22% or less per month, and the accrual alphas
are fairly modest as well, at 0.42% or less. The estimated illiquidity alphas, while not quite
significant at conventional levels, are nevertheless economically substantial, as high as 0.83%
per month. This latter result raises the power issue mentioned earlier. Also unlike the US,
there is no momentum effect in China. There is, however, a reversal effect, as past losers
significantly outperform past winners.
Reversal effects in China are especially strong. Past performance over any length window
tends to reverse in the future. In contrast, past returns in the US correlate in different
directions with future returns, depending on the length of the past-return window. That is,
past one-month returns correlate negatively with future returns, past two-to-twelve-month
returns correlate positively (the well-documented momentum effect), and past three-to-five-
year returns correlate negatively. In China, past returns over various windows all predict
future reversals. In untabulated results, we find that past returns over windows of one,
three, six, and twelve months, as well as five years, all negatively predict future returns, in
monotonically weakening magnitudes. For a one-month window of past return, the decile
of biggest losers outperforms the biggest winners with a CAPM alpha of 18% annually (t-
statistic: 2.96). The alpha drops to 6% and becomes insignificant (t-statistic: 0.90) when
sorting by past one-year return.
We choose one-month reversal for the anomaly in the reversal category. One potential
source of short-run reversals that does not appear to be related to this anomaly is bid-ask
bounce, e.g., Niederhoffer and Osborne (1966). The WIND data beginning in 2012 allow
us to average each stock’s best bid and ask prices at the day’s close of trading. Using
the resulting mid-price returns to compute the one-month reversal anomaly gives a result
virtually identical to (even slightly higher than) that obtained using closing-price returns:
2.21% versus 2.15% for the average long-short monthly return over the 2012–2016 subperiod.
Altogether we find ten significant anomalies. Table 6 reports their average excess returns
along with their CAPM alphas and betas. The results for the unconditional sorts appear in
Panel A. The monthly CAPM alphas range from 0.53%, for 12-month turnover, to 1.49%,
for one-month reversal, and most display significant t-statistics. The average alpha for the
ten anomalies is 1.02%, and the average t-statistic is 2.21.
18
Panel B of Table 6 reports the corresponding results for the size-neutral sorts. Two
differences from Panel A emerge. First, size-neutralization substantially increases the alphas
of several anomalies. For example, the ROE monthly alpha increases by 0.57%, the EP
alpha increases by 0.52%, and the alpha for twelve-month turnover increases by 0.21% bps.
Second, for almost all of the long-short spreads, standard deviations decrease and thus t-
statistics increase. The decrease in standard deviations confirms that size is an important risk
factor. The size-neutral sorting essentially gives the long-short spreads a zero SMB loading
and thus smaller residual variance in the single-factor CAPM regression. Panel B conveys
a similar message as Panel A, just more strongly: all ten anomalies generate significant
CAPM-adjusted return spreads. The average monthly CAPM alpha for the size-neutral
sorts is 1.17%, and the average t-statistic is 2.91.
6.2. Factor model explanations of anomalies
Table 7 reports CH-3 alphas and factor loadings for the ten anomalies that survive the
CAPM, the same anomalies as in Table 7. For the most part, our CH-3 model explains
the anomalies well. Panel A of Table 7 reports results for the unconditional sorts. Not
surprisingly, CH-3 explains the size anomaly. More noteworthy is that the model explains
all the value anomalies (EP, BM, and CP), which all load positively on our value factor.
The monthly CH-3 alphas of the three value anomalies are 0.64% or less, and the highest
t-statistic is just 1.02. These findings echo the earlier Fama-MacBeth regression results,
where EP subsumes both BM and CP in terms of cross-sectional abilities to explain average
returns.
Perhaps unexpectedly, given the US evidence, CH-3 fully explains the profitability anomaly,
ROE. In the US, profitability’s strong positive relation to average return earns it a position
as a factor in the models recently advanced by Hou et al. (2015) and Fama and French
(2015). In China, however, profitability is captured by our three-factor model. The ROE
spread loads heavily on the value factor (t-statistic: 9.43), and the CH-3 monthly alpha is
−0.36%, with a t-statistic of just −0.88.
CH-3 also performs well on the volatility anomalies. It produces insignificant alphas for
return spreads based on the past month’s daily volatility and the past month’s maximum
daily return (MAX). The CH-3 monthly alphas for both anomalies are 0.27% or less, with
t-statistics no higher than 0.65. We also see that both of the anomalies load significantly
on the value-factor. That is, low (high) volatility stocks behave similarly to value (growth)
stocks.
19
Recall from the previous subsection that the estimated CAPM alpha for the illiquidity
anomaly, while not quite clearing the statistical-significance hurdle, is as high as 0.83% per
month. In contrast, we find that the corresponding CH-3 alpha is just 0.23%, with at t-
statistic of 1.14. That is, if we were to add the illiquidity anomaly to our set of ten, given
its substantial estimated CAPM alpha, we see that illiquidity would also be included in the
list of anomalies that CH-3 explains.
To say for short that our CH-3 model “explains” an anomaly, as in several instances above,
must prompt a nod to the power issue mentioned earlier. Of course, more accurate would be
to say that the test presented by the anomaly merely fails to reject the model. In general,
however, the anomalies for which we can make this statement produce not only insignificant
t-statistics but also fairly small estimated CH-3 alphas. Across the eight anomalies that
the CH-3 model “explains,” the average absolute estimated monthly alpha is 0.30% in the
unconditional sorts and 0.26% in size-neutral sorts. In contrast, the same anomalies produce
average absolute FF-3 alphas of 0.84% and 0.90% in the unconditional and size-neutral sorts.
CH-3 encounters its limitations with anomalies in the reversal and turnover categories.
While the reversal spread loads significantly on SMB, its monthly alpha is nevertheless
0.93% (t-statistic:1.70). In the turnover category, CH-3 accommodates twelve-month turnover
well but has no success with abnormal one-month turnover. The latter anomaly’s return
spread has small and insignificant loadings on SMB and VMG, and its CH-3 monthly
alpha is 1.28%, nearly identical to its CAPM alpha (t-statistic: 2.86).
The size-neutral sorts, reported in Panel B of Table 7, deliver the same conclusions as the
unconditional sorts in Panel A. CH-3 again explains all anomalies in the value, profitability,
and volatility categories. The monthly alphas for those anomalies have absolute values of
0.61% or less, with t-statistics less than 0.98 in magnitude. For the reversal and turnover
categories, CH-3 displays the same limitations as in Panel A. The CH-3 monthly alpha for
reversal is 1.13%, with a t-statistic of 2.12. Abnormal turnover has an alpha of 1.24%, with
a t-statistic of 3.04.
In the same format as Table 7, Table 8 reports the corresponding results for the FF-3
model. These results clearly demonstrate that FF-3 performs substantially worse than CH-3,
leaving significant anomalies in five of the six categories—all categories except size. Consider
the results in Panel A, for example. Similar to FF-3’s inability to price our EP-based value
factor, FF-3 fails miserably with the EP anomaly, leaving a monthly alpha of 1.54% (t-
statistic: 5.57). Moreover, as in the US, FF-3 cannot accommodate profitability. The ROE
anomaly leaves a monthly alpha of 1.75% (t-statistic: 5.67). Finally, for all anomalies in the
20
volatility, reversal and turnover categories, FF-3 leaves both economically and statistically
significant alphas.
Table 9 compares the abilities of models to explain anomalies by reporting the average
absolute alphas for the anomaly long-short spreads, the corresponding average absolute t-
statistics, and GRS tests of whether a given model produces jointly zero alphas across anoma-
lies. The competing models include unconditional means (i.e., zero factors), the single-factor
CAPM, and both of the three-factor models, CH-3 and FF-3. As in Tables 7 and 8, Panel
A reports results for the unconditional sorts, and Panel B reports the size-neutral sorts.
First, in both panels, observe that CH-3 produces much smaller absolute alphas than do the
other models: 0.45% for CH-3 versus at least 0.9% for the other models. In Panel A, for the
unconditional sorts, the GRS p-value of 0.15 for CH-3 fails to reject the joint hypothesis that
all ten anomalies produce zero CH-3 alphas. In contrast, the corresponding p-values for the
other models are all less than 10−4. For the size-neutral sorts (Panel B), a similar disparity
occurs for a test of jointly zero alphas on nine anomalies (size is omitted). The CH-3 p-value
is 0.05 versus p-values less than 10−4 for the other models. Because size, EP , and BM are
used to construct factors, we also eliminate those three anomalies and conduct the GRS test
using the remaining seven. As shown in the last two rows of each panel, the results barely
change—CH-3 again dominates.
7. A four-factor model in China
Notwithstanding the impressive performance of CH-3, the model does leave significant alphas
for reversal and turnover anomalies, as noted earlier. Of course, we see above that these
anomalies are not troublesome enough to cause the larger set that includes them to reject
CH-3 when accounting for the multiple comparisons inherent in the GRS test. At the same
time, however, the latter test confronts the same power issue discussed earlier. Moreover, the
reversal and turnover anomalies both produce alpha estimates that are not only statistically
significant but also economically large, over 1% per month in the size-neutral sorts reported
in Panel B of Table 7. We therefore explore the addition of a fourth factor based on turnover.
In subsection 7.1, we discuss this turnover factor’s sentiment-based motivation, describe the
factor’s construction, and explain how we also modify the size factor when building the four-
factor model, CH-4. Subsection 7.2 then documents CH-4’s ability to explain all of China’s
21
reported anomalies.
7.1. A turnover factor
A potential source of high trading intensity in a stock is heightened optimism toward
the stock by sentiment-driven investors. This argument is advanced by Baker and Stein
(2004), for example, and Lee (2013) uses turnover empirically as a sentiment measure at
the individual-stock level. High sentiment toward a stock can affect its price, driving it
higher than justified by fundamentals and thereby lowering its expected future return. Two
assumptions underly such a scenario. One is a substantial presence in the market of irrational,
sentiment-driven traders. The other is the presence of short-sale impediments.
China’s stock market is especially suited to both assumptions. First, individual retail
investors are the most likely sentiment traders, and individual investors are the major partic-
ipants in China’s stock market. As of year-end 2015, over 101 million individuals had trading
accounts, and individuals held 88% of all free-floating shares (Jiang, Qian, and Gong, 2016).
Second, shorting is extremely costly in China (China Securities Regulatory Commission,
2008).
Shorting constraints not only impede the correction of overpricing. They also sign the
likely relation between sentiment and turnover. As Baker and Stein (2004) argue, when
pessimism about a stock prevails among sentiment-driven investors, those who do not already
own the stock simply do not participate in the market, as short-sale constraints prevent them
from acting on their pessimistic views. In contrast, when optimism prevails, sentiment-driven
investors can participate broadly in buying the stock. Thus, shorting constraints make high
turnover (greater liquidity) more likely to accompany strong optimism as opposed to strong
pessimism.
Given this sentiment-based motivation, to construct our fourth factor we use abnormal
turnover, which is the past month’s share turnover divided by the past year’s turnover. We
construct this turnover factor in precisely the same manner as our value factor, again neu-
tralizing with respect to size. That is, abnormal turnover simply replaces EP , except the
factor goes long the low-turnover stocks, about which investors are relatively pessimistic, and
goes short the high-turnover stocks, for which greater optimism prevails. We denote the re-
sulting factor PMO (Pessimistic Minus Optimistic). We also construct a new SMB, taking
a simple average of the EP -neutralized version of SMB from CH-3 and the corresponding
turnover-neutralized version. The latter procedure for modifying SMB when adding addi-
22
tional factors essentially follows Fama and French (2015). The new size and turnover factors
have annualized averages of 11% and 12%. The market and value factors in CH-4 are the
same as in CH-3.
7.2. Explaining all anomalies with four factors
For model CH-4, Table 10 reports results of the same analyses conducted for models CH-3
and FF-3 and reported in Tables 7 and 8. Adding the fourth factor produces insignificant
alphas not just for the abnormal-turnover anomaly but also for reversal. In Panel A, for
the unconditional sorts, the CH-4 monthly alphas for those anomalies are 0.00% and 0.49%,
with t-statistics of −0.01 and 0.87. The size-neutral sorts in Panel B produce similar results.
Adding the turnover factor essentially halves the reversal anomaly’s unconditional alpha
relative to its CH-3 value in Table 7, even though the rank correlation across stocks between
the sorting variables for the turnover and reversal anomalies is just 0.3 on average.
CH-4 accommodates the above two anomalies, thus now explaining all ten, while also
lowering the average magnitude of all the alphas. For the unconditional sorts, the average
absolute alpha drops to 0.30%, versus 0.45% for CH-3, and the average absolute t-statistic
drops to 0.69, versus 1.12 for CH-3. The GRS test of jointly zero alphas for all ten anomalies
produces a p-value of 0.41, versus 0.15 for CH-3, thereby moving even farther from rejecting
the null. Similar improvements occur for the size-neutral sorts.
8. Conclusions
Size and value are important factors in the Chinese stock market, with both having average
premiums exceeding 12% per year. Capturing these factors well, however, requires that one
not simply replicate the Fama and French (1993) procedure developed for the US.
Unlike small listed stocks in the US, China’s tight IPO constraints cause returns on the
smallest stocks in China to be significantly contaminated by fluctuations in the value of be-
coming corporate shells in reverse mergers. To avoid this contamination, before constructing
factors we eliminate the smallest 30% of stocks, which account for just 7% of the market’s
total capitalization. Eliminating these stocks yields factors that perform substantially bet-
ter than using all listed stocks to construct factors, whereas the Fama and French (1993)
procedure essentially does the latter in the US.
23
Value effects in China are captured much better by the earning-price ratio (EP ) than by
the book-to-market ratio (BM) used in the US by Fama and French (1993). The superiority
of EP in China is demonstrated at least two ways. First, in an investigation paralleling
Fama and French (1992), cross-sectional regressions reveal that EP subsumes other valuation
ratios, including BM , in explaining average stock returns. Second, our three-factor model,
CH-3, with its EP -based value factor, dominates the alternative FF-3 model, with its BM -
based value factor. In a head-to-head model comparison, CH-3 prices both the size and
value factors in FF-3, whereas FF-3 prices neither of the size and value factors in CH-3. In
particular, FF-3 leaves a 17% annual alpha for our value factor.
We also survey the literature that documents return anomalies in China, and we find
ten anomalies with significant CAPM alphas in our sample. Our CH-3 model explains eight
of the anomalies, including not just all value anomalies but also profitability and volatility
anomalies not explained in the US by the three-factor Fama-French model. In contrast, the
only two anomalies in China that FF-3 explains are size and BM. The two anomalies for
which CH-3 fails, return reversal and abnormal turnover, are both explained by a four-factor
model that adds a sentiment-motivated turnover factor.
24
1 2 3 4 5 6 7 8 9 10
Size decile
0.0
0.2
0.4
0.6
Fra
ctio
n
Fig. 1. Firm Size Distribution of Reverse-Merger Shells. The figure displays the size distribution offirms acquired in reverse-merger deals from January 2007 through December 2016. A total of 133reverse-merger deals occurred, and the fraction of those deals falling into a given firm size decile isdisplayed in the bar chart. Size deciles reflect month-end market values three months before thedeal month.
25
Panel A. Ratio of Estimated Shell Value to Market Cap
2009 2010 2011 2012 2013 2014 2015 2016 2017
0.0
0.2
0.4
0.6
0.8
1.0
Ratio
Panel B. Estimated Shell Value (RMB)
2009 2010 2011 2012 2013 2014 2015 2016 2017
0
500
1000
1500
She
ll val
ue (m
illion
s of
RM
B)
Fig. 2. Shell Values Over Time. Panel A displays the time series of the ratio of estimated shellvalue to firm market capitalization. Panel B displays the time series of the estimated shell value(in RMB). The sample period is January 2009 through December 2016.
26
Table 1Return reactions to earnings surprises across different size groups in China and the US
The table reports slope estimates and R-squares in a panel regression of earnings-window returns onearnings surprises,
Ri,t−k,t+k = a+ b SUEi,t + ei,t,
where earnings are announced on day t, Ri,t−k,t+k is the cumulative return on stock i, in excess of the marketreturn, over the surrounding trading days from t − k through t + k, SUEi,t = ∆i,t/σ(∆i), ∆i,t equals theyear-over-year change in stock i’s quarterly earnings, and σ(∆i) is the standard deviation of ∆i,t for the lasteight quarters. Panel A contains results for k = 0; Panel B contains results for k = 3. The regression isestimated within each of three size groups in both the China and US markets. The groups are formed basedon the top 30%, middle 40% and bottom 30% of the previous month’s market capitalizations. The sampleperiods are January 2000 through December 2016 for China and January 1980 through December 2016 forthe US. The US returns data are from CRSP and the earnings data are from COMPUSTAT. White (1980)heteroscedasticity-consistent t-statistics are reported in parentheses. The estimates of b are multiplied by 100.
China US
Quantity Smallest Middle Largest Smallest Middle Largest
Panel A: k = 0
b 0.14 0.17 0.24 0.19 0.07 0.05
(6.34) (12.42) (17.28) (7.51) (6.99) (9.90)
R2 0.003 0.010 0.017 0.005 0.003 0.002
Panel B: k = 3
b 0.43 0.58 0.59 0.52 0.20 0.13
(9.74) (17.91) (17.60) (7.84) (6.03) (10.68)
R2 0.006 0.016 0.021 0.012 0.005 0.003
27
Table
2F
ama-M
acB
eth
regre
ssio
ns
ofst
ock
retu
rns
onb
eta,
size
,an
dva
luat
ion
rati
os
Th
eta
ble
rep
orts
aver
age
slop
eco
effici
ents
from
month
-by-m
onth
Fam
a-M
acB
eth
regre
ssio
ns.
Ind
ivid
ual
stock
retu
rns
are
regre
ssed
cross
-se
ctio
nal
lyon
stock
char
acte
rist
ics
asof
the
pre
vio
us
month
.T
he
colu
mn
sco
rres
pon
dto
diff
eren
tre
gre
ssio
nsp
ecifi
cati
on
s,w
ith
non
-em
pty
row
sin
dic
atin
gth
ein
clu
ded
regr
esso
rs.
Th
ere
gres
sors
incl
ud
e:p
rera
nkin
gC
AP
Mβt
esti
mate
du
sin
gpast
12
month
sof
dail
yre
turn
sw
ith
five
-lag
Dim
son
(197
9)co
rrec
tion
,lo
gm
onth
-en
dm
arke
tca
p(l
ogM
),b
ook-t
o-m
ark
et(l
ogBM
),ass
ets-
to-m
ark
et(l
ogAM
),EP
+,
wh
ich
equ
als
the
posi
tive
valu
esof
earn
ings
-to-
pri
cean
dze
root
her
wis
e,D
(EP<
0),
wh
ich
equ
als
on
eif
earn
ings
are
neg
ati
vean
dze
rooth
erw
ise,CP
+,
an
dD
(CP<
0)
(wit
hth
ela
sttw
osi
mil
arly
defi
ned
).T
he
last
row
rep
orts
the
aver
age
ad
just
edR
-squ
are
dfo
rea
chsp
ecifi
cati
on
.T
he
sam
ple
per
iod
isJanu
ary
2000
thro
ugh
Dec
emb
er20
16.
Th
et-
stat
isti
csb
ased
onN
ewey
an
dW
est
(1987)
stan
dard
erro
rsw
ith
fou
rla
gs
are
rep
ort
edin
pare
nth
eses
.
Qu
anti
ty(1
)(2
)(3
)(4
)(5
)(6
)(7
)(8
)(9
)
Inte
rcep
t0.0
149
0.05
810.
0571
0.06
590.
0629
0.06
900.0
564
0.0
716
0.072
8
(1.9
4)(3
.32)
(3.1
9)(3
.90)
(3.7
4)(4
.03)
(3.1
9)(4
.40)
(4.3
9)
β−
0.00
02
−0.
0010
−0.
0018
−0.
0017
0.00
02−
0.001
0−
0.0
002
−0.
000
4
(−0.0
9)
(−0.
37)
(−0.
71)
(−0.
67)
(0.0
7)(−
0.37)
(−0.0
6)
(−0.
15)
logME
−0.
0049
−0.
0046
−0.
0046
−0.
0048
−0.
0068
−0.0
047
−0.
006
6−
0.0
064
(−2.
91)
(−2.
69)
(−2.
73)
(−3.
00)
(−4.
34)
(−2.8
0)
(−4.
49)
(−4.4
0)
logBM
0.00
570.0
022
0.0
035
(3.2
1)(1
.31)
(1.7
6)
logAM
0.00
450.
001
4
(3.0
3)(0
.99)
EP
+0.
9503
0.782
50.
796
0
(4.8
8)(4
.38)
(5.0
6)
D(EP<
0)0.
0006
−0.0
005
−0.
000
1
(0.3
1)(−
0.2
9)
(−0.
04)
CP
+0.0
546
0.0
181
(3.4
1)(1
.35)
D(CP<
0)
0.001
90.
001
6
(3.1
1)(2
.37)
R2
0.0
196
0.02
770.
0441
0.06
520.
0677
0.06
150.0
454
0.0
832
0.077
6
28
Table 3Summary statistics for the CH-3 factors
This table reports the means, standard deviations, t-statistics, and pairwise correlations for the threefactors in the CH-3 model. The means and standard deviations are expressed in percent per month. Thesample period is January 2000 through December 2016 (204 months).
Correlations
Factor Mean Std. Dev. t-stat. MKT SMB VMG
MKT 0.66 8.09 1.16 1.00 0.12 −0.27SMB 1.03 4.52 3.25 0.12 1.00 −0.62VMG 1.14 3.75 4.34 −0.27 −0.62 1.00
29
Table 4Average R-squares for individual stocks in China and the US
The table compares the average R-squares in regressions of monthly individual stocks’ returns on factorsin China’s and US stock markets. Regressions are estimated for four models: one with just the excessmarket return (MKT ); one with MKT plus the size-factor; one with MKT plus value factor; and the three-factor model with market plus size and value factors. In China’s stock market, we use our CH-3 model’smarket(MKT ), size (SMB) and value (VMG) factors while in the US market, we stick to FF-3’s threefactors, market, SMB and BM-based HML. For each stock, we run rolling-window regressions of eachstock’s monthly returns on factors over the past 3 years (12 months), and then average r-squares across timesfor each stock first and take the average of these averages across all stocks. In Panel A, we report averager-square across all individual stocks in China’s main boards and GEM (including bottom 30% of stocks). InPanel B, we report the average of all but the smallest 30% stocks’ r-squares (excluding the bottom 30%), andin Panel C, we report the average r-square of all common stocks from NYSE, AMEX and NASDAQ for theUS. The sample periods for both China and US market are from January 2000 through December 2016 (204months).
Factors Avg. R-square
Panel A: All individual stocks in China
MKT 0.385MKT , SMB 0.507MKT , VMG 0.471MKT , SMB, VMG 0.536
Panel B: All but the smallest 30% of stocks in China
MKT 0.417MKT , SMB 0.528MKT , VMG 0.501MKT , SMB, VMG 0.562
Panel C: All individual stocks in the US
MKT 0.177MKT , SMB 0.231MKT , HML 0.226MKT , SMB, HML 0.273
30
Table 5Abilities of models CH-3 and FF-3 to explain each other’s size and value factors
Panel A reports a factor’s estimated monthly alpha (in percent) with respect to the other model (withWhite, 1980, heteroscedasticity-consistent t-statistics in parentheses). Panel B computes the Gibbons-Ross-Shanken(1989) F -test of whether a given model produces zero alphas for the factors of the other model (p-valuein parentheses). The sample period is January 2000 through December 2016.
Alphas with respect to:
Factors CH-3 FF-3
Panel A: Alpha (t-statistic)
FFSMB -0.04 -(-0.66) -
FFHML 0.34 -(0.97) -
SMB - 0.47- (7.03)
VMG - 1.39- (7.93)
Panel B: GRS F -statistics (p-value)
FFSMB, FFHML 0.88 -
(0.41) -
SMB, VMG - 33.90- (2.14× 10−13)
31
Table 6CAPM alphas and betas for anomalies
For each of ten anomalies, the table reports the monthly long-short return spread’s, average (R), CAPMalpha (α), and CAPM beta (β). In Panel A, for the unconditional sorts, the long leg of an anomaly is thevalue-weighted portfolio of stocks in the lowest decile of the anomaly measure, and the short leg containsthe stocks in the highest decile, where a high value of the measure is associated with lower return. In PanelB, long/short legs are neutralized with respect to size. That is, we first form size deciles by sorting on theprevious month’s market value. Within each size decile, we then create ten deciles formed by sorting on theanomaly variable. Finally, we form the anomaly’s decile portfolios, with each portfolio pooling the stocks ina given anomaly decile across the size groups, again with value weighting. Panel B omits the size anomaly,whose alpha equals zero by construction with size-neutral sorts. Our sample period is January 2000 throughDecember 2016 (204 months). All t-statistics are based on the heteroscedasticity-consistent standard errors ofWhite (1980).
Category Anomaly R α β t(R) t(α) t(β)
Panel A: Unconditional Sorts
Size Market Cap 1.09 0.97 0.18 1.92 1.81 1.90Value EP 1.27 1.37 −0.16 2.58 2.93 −2.15Value BM 1.14 1.14 0.01 2.08 2.13 0.06Value CP 0.73 0.70 0.04 1.67 1.69 0.55Profitability ROE 0.83 0.93 −0.15 1.77 2.11 −2.09Volatility 1−Month Vol. 0.81 1.03 −0.34 1.64 2.31 −5.55Volatility MAX 0.57 0.81 −0.36 1.26 2.02 −6.39Reversal 1−Month Return 1.47 1.49 −0.02 2.96 3.06 −0.22Reversal 12−Mon Turn. 0.33 0.53 −0.29 0.63 1.09 −3.46Turnover 1−Mo. Abn. Turn. 1.14 1.27 −0.19 2.44 2.92 −2.66
Panel B: Size-Neutral Sorts
Value EP 1.80 1.89 −0.14 4.32 4.72 −2.25Value BM 1.14 1.10 0.05 2.23 2.22 0.64Value CP 0.78 0.76 0.04 2.27 2.25 0.71Profitability ROE 1.45 1.50 −0.07 3.90 4.11 −1.30Volatility 1−Month Vol. 0.66 0.90 −0.37 1.41 2.19 −6.20Volatility MAX 0.39 0.60 −0.32 0.93 1.61 −6.14Reversal 1−Month Return 1.67 1.65 0.02 3.65 3.68 0.32Reversal 12−Mon Turn. 0.51 0.74 −0.34 1.06 1.74 −4.94Turnover 1−Mo. Abn. Turn. 1.29 1.39 −0.15 3.19 3.68 −2.56
32
Table 7CH-3 alphas and factor loadings for anomalies
For each of ten anomalies, the table reports the monthly long-short return spread’s CH-3 alpha and factor loadings. For eachanomaly, the regression estimated is
Rt = α+ βMKTMKTt + βSMBSMBt + βVMGVMGt + εt,
where Rt is the anomaly’s long-short return spread in month t, MKTt is the excess market return, SMBt is CH-3’s sizefactor, and VMGt is the EP -based value factor. In Panel A, for the unconditional sorts, the long leg of an anomaly is thevalue-weighted portfolio of stocks in the lowest decile of the anomaly measure, and the short leg contains the stocks in thehighest decile, where a high value of the measure is associated with lower return. In Panel B, long/short legs are neutralizedwith respect to size. That is, we first form size deciles by sorting on the previous month’s market value. Within each sizedecile, we then create ten deciles formed by sorting on the anomaly variable. Finally, we form the anomaly’s decile portfolios,with each portfolio pooling the stocks in a given anomaly decile across the size groups, again with value weighting. Panel Bomits the size anomaly, whose alpha equals zero by construction with size-neutral sorts. Our sample period is January 2000through December 2016. All t-statistics are based on the heteroscedasticity-consistent standard errors of White (1980).
Category Anomaly α βMKT βSMB βVMG t(α) t(βMKT ) t(βSMB) t(βVMG)
Panel A: Unconditional Sorts
Size Market Cap 0.21 0.01 1.45 −0.54 1.71 0.77 40.88 −11.70Value EP 0.04 0.04 −0.38 1.40 0.16 1.31 −4.73 14.75Value BM 0.64 0.06 −0.03 0.43 1.02 0.65 −0.14 1.64Value CP 0.20 0.14 −0.28 0.64 0.45 2.10 −1.95 4.00Profitability ROE −0.36 0.03 −0.29 1.28 −0.88 0.70 −2.35 9.43Volatility 1−Month Vol. 0.23 −0.23 −0.12 0.75 0.44 −3.81 −0.67 3.86Volatility MAX 0.27 −0.30 −0.05 0.48 0.65 −4.57 −0.30 2.55Reversal 1−Month Return 0.93 −0.06 0.56 0.01 1.70 −0.69 3.15 0.03Turnover 12−Month Turn. 0.42 −0.14 −0.85 0.77 1.30 −3.69 −9.33 7.90Turnover 1−Mo. Abn. Turn. 1.28 −0.22 0.18 −0.16 2.86 −2.78 0.93 −0.76
Panel B: Size-Neutral Sorts
Value EP 0.23 0.02 0.05 1.32 0.82 0.47 0.57 11.97Value BM 0.61 0.13 −0.15 0.53 0.98 1.60 −0.80 2.19Value CP 0.18 0.11 −0.06 0.52 0.54 1.98 −0.50 3.84Profitability ROE −0.37 0.05 0.41 1.20 −1.04 1.23 4.14 9.66Volatility 1−Month Vol. 0.20 −0.28 −0.08 0.64 0.42 −4.96 −0.49 3.34Volatility MAX 0.00 −0.26 0.05 0.45 0.00 −4.38 0.30 2.50Reversal 1−Month Return 1.13 0.01 0.41 0.10 2.12 0.11 2.59 0.55Turnover 12−Month Turn. 0.25 −0.22 −0.43 0.74 0.69 −4.94 −3.91 5.74Turnover 1−Mo. Abn. Turn. 1.24 −0.18 0.25 −0.08 3.04 −2.79 1.55 −0.43
33
Table 8FF-3 alphas and factor loadings for anomalies
For each of ten anomalies, the table reports the monthly long-short return spread’s CH-3 alpha and factor loadings. For eachanomaly, the regression estimated is
Rt = α+ βMKTMKTt + βSMBFFSMBt + βHMLFFHMLt + εt,
where Rt is the anomaly’s long-short return spread in month t, MKTt is the excess market return, SMBt is FF-3’s sizefactor, and FFHMLt is the BM -based value factor. In Panel A, for the unconditional sorts, the long leg of an anomaly isthe value-weighted portfolio of stocks in the lowest decile of the anomaly measure, and the short leg contains the stocks in thehighest decile, where a high value of the measure is associated with lower return. In Panel B, long/short legs are neutralizedwith respect to size. That is, we first form size deciles by sorting on the previous month’s market value. Within each sizedecile, we then create ten deciles formed by sorting on the anomaly variable. Finally, we form the anomaly’s decile portfolios,with each portfolio pooling the stocks in a given anomaly decile across the size groups, again with value weighting. Panel Bomits the size anomaly, whose alpha equals zero by construction with size-neutral sorts. Our sample period is January 2000through December 2016. All t-statistics are based on the heteroscedasticity-consistent standard errors of White (1980).
Category Anomaly α βMKT βSMB βHML t(α) t(βMKT ) t(βSMB) t(βHML)
Panel A: Unconditional Sorts
Size Market Cap 0.16 0.04 1.55 −0.11 1.36 1.86 34.29 −2.43Value EP 1.54 −0.07 −0.98 0.48 5.57 −1.63 −13.29 6.54Value BM −0.28 0.00 0.12 1.60 −1.25 0.09 1.48 30.61Value CP 0.63 0.08 −0.49 0.43 1.40 1.31 −3.84 2.31Profitability ROE 1.75 −0.06 −1.01 −0.28 5.67 −1.36 −12.74 −3.08Volatility 1−Month Vol. 0.83 −0.30 −0.40 0.52 2.11 −5.41 −3.07 4.18Volatility MAX 0.74 −0.33 −0.28 0.28 1.85 −5.70 −1.79 1.96Reversal 1−Month Return 0.94 −0.06 0.53 0.28 1.97 −0.83 3.50 1.58Turnover 12−Month Turn. 0.83 −0.19 −1.08 0.38 2.96 −4.97 −13.10 3.72Turnover 1−Mo. Abn. Turn. 1.34 −0.21 0.16 −0.20 2.86 −2.76 0.95 −0.99
Panel B: Size-Neutral Sorts
Value EP 1.76 −0.09 −0.53 0.52 5.49 −1.79 −6.52 6.17Value BM −0.01 0.07 −0.10 1.39 −0.04 1.75 −1.36 20.12Value CP 0.52 0.06 −0.23 0.44 1.73 1.33 −2.33 4.05Profitability ROE 2.01 −0.04 −0.36 −0.35 5.72 −0.71 −3.75 −3.38Volatility 1−Month Vol. 0.76 −0.33 −0.33 0.40 2.06 −6.04 −2.64 3.47Volatility MAX 0.43 −0.30 −0.16 0.31 1.14 −5.67 −1.10 2.60Reversal 1−Month Return 1.21 −0.01 0.35 0.29 2.55 −0.09 2.63 1.78Turnover 12−Month Turn. 0.80 −0.28 −0.68 0.39 2.46 −5.89 −6.37 3.74Turnover 1−Mo. Abn. Turn. 1.37 −0.17 0.21 −0.12 3.26 −2.82 1.43 −0.68
34
Table 9Comparing the abilities of models to explain anomalies
The table reports measures summarizing the degree to which anomalies produce alphas under three differentfactor models: CAPM, FF-3, and CH-3. Also reported are measures for “unadjusted” return spreads (i.e., fora model with no factors). For each model, the table reports the average absolute monthly alpha (in percent),average absolute t-statistic, the Gibbons, Ross, and Shanken (1989) “GRS” F -statistic with associated p-value,and the number of anomalies for which the model produces the smallest absolute alpha among the four models.In Panel A, for the unconditional sorts, the long leg of an anomaly is the value-weighted portfolio of stocks inthe lowest decile of the anomaly measure, and the short leg contains the stocks in the highest decile, wherea high value of the measure is associated with lower return. In Panel B, long/short legs are neutralized withrespect to size. That is, we first form size deciles by sorting on the previous month’s market value. Withineach size decile, we then create ten deciles formed by sorting on the anomaly variable. Finally, we form theanomaly’s decile portfolios, with each portfolio pooling the stocks in a given anomaly decile across the sizegroups, again with value weighting. Two versions of the GRS test are reported. In Panel A, GRS10 uses all tenanomalies, while GRS7 excludes the anomalies for size, BM , and EP , which are variables used to constructfactors. Panel B omits the size anomaly, whose alpha equals zero by construction with size-neutral sorts. Allt-statistics are based on the heteroscedasticity-consistent standard errors of White (1980). The sample periodis from January 2000 through December 2016 (204 months).
Measure Unadjusted CAPM FF-3 CH-3
Panel A: Unconditional Sorts
Average |α| 0.94 1.02 0.90 0.45Average |t| 1.89 2.21 2.70 1.12
GRS10 7.30 7.31 6.00 1.49p10 <0.0001 <0.0001 <0.0001 0.15
GRS7 4.40 4.45 6.86 1.74p7 0.0002 0.0001 0.0001 0.10
Panel B: Size-Neutral Sorts
Average |α| 1.08 1.17 0.99 0.47Average |t| 2.55 2.91 2.72 1.07
GRS9 8.24 8.08 7.97 1.97p9 <0.0001 <0.0001 <0.0001 0.05
GRS7 8.15 8.10 9.11 2.33p7 <0.0001 <0.0001 <0.0001 0.03
35
Table
10
An
om
aly
alp
has
und
era
fou
r-fa
ctor
mod
el
For
each
ofte
nan
omal
ies,
the
tab
lere
por
tsth
em
onth
lylo
ng-s
hort
retu
rnsp
read
’sC
H-4
alp
ha
an
dfa
ctor
load
ings.
For
each
an
om
aly
,th
ere
gre
ssio
nes
tim
ated
isR
t=α
+βM
KTMKTt
+βSM
BSMB
t+βVM
GVMG
t+βPM
OPMO
t+ε t,
wh
ereR
tis
the
anom
aly’s
lon
g-sh
ort
retu
rnsp
read
inm
ontht,MKTt
isth
eex
cess
mark
etre
turn
,SMB
tis
CH
-3’s
size
fact
or,VMG
tis
theEP
-base
dva
lue
fact
or,
andPMO
t(P
essi
mis
tic
min
us
Op
tim
isti
c)is
the
senti
men
tfa
ctor
base
don
ab
norm
al
turn
over
.In
Pan
elA
,fo
rth
eu
nco
ndit
ion
al
sort
s,th
elo
ng
leg
ofan
anom
aly
isth
eva
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wei
ghte
dp
ort
foli
oof
stock
sin
the
low
est
dec
ile
of
the
anom
aly
mea
sure
,an
dth
esh
ort
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ins
the
stock
sin
the
hig
hes
td
ecil
e,w
her
ea
hig
hva
lue
ofth
em
easu
reis
ass
oci
ate
dw
ith
low
erre
turn
.In
Pan
elB
,lo
ng/sh
ort
legs
are
neu
trali
zed
wit
hre
spec
tto
size
.T
hat
is,
we
firs
tfo
rmsi
zed
ecil
esby
sort
ing
on
the
pre
vio
us
month
’sm
ark
etva
lue.
Wit
hin
each
size
dec
ile,
we
then
crea
tete
ndec
iles
form
edby
sort
ing
onth
ean
omal
yva
riab
le.
Fin
ally
,w
efo
rmth
ean
om
aly
’sd
ecil
ep
ort
foli
os,
wit
hea
chp
ort
foli
op
ooli
ng
the
stock
sin
agiv
enan
om
aly
dec
ile
acro
ssth
esi
zegr
oup
s,ag
ain
wit
hva
lue
wei
ghti
ng.
Pan
elB
om
its
the
size
an
om
aly
,w
hose
alp
ha
equ
als
zero
by
con
stru
ctio
nw
ith
size
-neu
tral
sort
s.O
ur
sam
ple
per
iod
isJan
uar
y20
00th
rou
ghD
ecem
ber
2016.
Allt-
stati
stic
sare
base
don
the
het
erosc
edast
icit
y-c
on
sist
ent
stan
dard
erro
rsof
Wh
ite
(198
0).
Cate
gory
An
omaly
αβMKT
βSMB
βVMG
βPMO
t(α
)t(βMKT
)t(βSMB
)t(βVMG
)t(βPMO
)
Panel
A:UnconditionalSorts
Siz
eM
ark
etC
ap0.2
30.
051.
50−
0.42
0.01
1.41
3.0
539
.38
−6.8
80.1
7V
alu
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47
Panel
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36
Appendix
Section A.1 provides details of the data sources and the filters we apply. Section A.2details the anomalies and their construction. Section A.3 provides further details aboutChina’s IPO review process. Section A.4 explains the reverse-merger data and the shell-value estimation, while section A.5 examines the hypothesis that the smallest 30% of stockscovary more with shell-value proxies. Section A.6 reports the results of recomputing theregressions reported in Table 2 with financial firms excluded. Section A.7 presents additionalcomparisons of model CH-3 to models FF-3 and FF-5.
A.1. Data sources and filters
Our stock trading data and firm financial data all come from WIND. Our sample includesall A-share stocks from the main boards of the Shanghai and Shenzhen exchanges as well asthe board of the GEM (Growth Enterprises Market), essentially the Chinese counterpart ofNASDAQ. In China, stock tickers for listed firms are non-reusable unique identifiers. Theticker contains six digits, of which the first two indicate the exchange and the security type.We include stocks whose first two digits are 60, 30, and 00. Our series for the riskfree rate,the one-year deposit rate, is obtained from the CSMAR database on WRDS. Our sampleperiod is January 2000 through December 2016.
We also impose several filters: First, we exclude stocks that have become public withinthe past six months. Second, we exclude stocks having less than 120 days of trading recordsduring the past 12 months. We also exclude stocks having less than 15 days of tradingrecords during the most recent month. The above filters are intended to prevent our resultsfrom being influenced by returns that follow long trading suspensions. Third, for the reasonexplained in Section 3, we eliminate the bottom 30% of stocks ranked by market capital-ization at the end of the previous month. Market capitalization is calculated as the closingprice times total shares outstanding, including non-tradable shares.
When we use financial-statement information to sort stocks, in constructing either factorsor anomaly portfolios, the sort at the end of a given month uses the information in a firm’sfinancial report having the most recent public release date prior to that month’s end. (TheWIND data include release dates.) Firms’ financial statement data are from quarterly reportsbeginning January 1, 2002, when public firms were required to report quarterly. Prior tothat date, our financial statement data are from semi-annual reports.
A.2. Firm characteristics and anomaly portfolios
We survey the literature documenting anomalies in China, and we compile here, to ourknowledge, an exhaustive list of stock characteristics identified as cross-sectional predictorsof future returns. The list comprises nine categories: size, value, profitability, volatility,investment, accruals, illiquidity, reversal, and turnover. Within each category, one or morefirm-level characteristics are identified as return predictors. The anomalies, by category, areas follows;
37
1. Size. The stock’s market capitalization is used in this category. It is computed as theprevious month’s closing price times total A-share outstanding, including non-tradableshares.4
2. Value. Three variables are used.
• Earnings-price ratio (EP ). Earnings equals the most recently reported net profitexcluding non-recurrent gains/losses. A stock’s EP is the ratio of earnings to theproduct of last month-end’s close price and total shares.
• Book-to-market ratio (BM). Book equity equals total shareholder equity minusthe book value of preferred stocks. A stock’s BM is the ratio of book equity tothe product of last month-end’s close price and total shares.
• Cash-flow-to-price (CP ). Cash flow equals the net change in cash or cash equiv-alents between the two most recent cash-flow statments.5 A stock’s CP is theratio of cash flow to the product of last month-end’s close price and total shares.
3. Profitability. Firm-level ROE at the quarterly frequency is used. The value of ROEequals the ratio of a firm’s earnings to book equity, with earnings and book equitydefined above.
4. Volatility. Two variables are used.
• One-month volatility. A firm’s one-month volatility is calculated as the standarddeviation of daily returns over the past 20 trading days.
• MAX. MAX equals the highest daily return over the previous month.
5. Investment. As in Fama and French (2015), a firm’s investment is measured by itsannual asset growth rate. Specifically, a firm’s asset growth equals total assets in themost recent annual report divided by total assets in the previous annual report.
6. Accruals. Two variables are used.
• Accruals. We construct firm-level accruals following Sloan (1996). Specifically, afirm’s accruals in year t can be expressed as:
Accrual = (∆CA−∆Cash)− (∆CL−∆STD −∆TP )−Dep
where ∆CA equals the most recent year-to-year change in current assets, ∆Cashequals the change in cash or cash equivalents, ∆CL equals the change in currentliabilities, ∆STD equals the change in debt included in current liabilities, ∆TPequals the change in income taxes payable, and Dep equals the most recent year’sdepreciation and amortization expenses.
4In China’s stock market, a firm could issue three types of share classes: A, B and H shares. Domesticinvestors are only allowed to trade A shares while foreign investors can only trade B shares. H shares areissued by domestic companies but traded in HK exchanges. We measure market size based total a-sharesbut measure valuation ratios scaled by total shares including B and H shares (assume earnings/book-valuesof a firm are shared by all its shareholders including foreign and Hongkong investors).
5Prior to January 2002, cash flow equals half the net change between the two most recent semi-annualstatements.
38
• Net-operating-assets (NOA). We construct firm-level NOA, following Hirshleifer,Hou, Teoh, and Zhang (2004). Specifically, NOA is calculated as:
NOA = (Operating Assett −Operating Liabilityt)/Total Assett−1
where Operating Assett equals total assets minus cash and short-term investment,Operating Liabilityt equals total assets minus short-term debt, long-term debt,minority interest, book preferred stock, and book common equity.
7. Illiquidity. We compute a stock’s average daily illiquidity over the past 20 tradingdays. Following Amihud (2002), a stock’s illiquidity measure for day t is calculated as
Illiqt = |rett|/volumet
where |rett| is the stock’s absolute return on day t, and volumet is the stock’s dollartrading volume on day t.
8. Turnover. Two variables are used.
• Twelve-month turnover. We measure twelve-month turnover as the average dailyshare turnover over the past 250 days. A firm’s daily turnover is calculated as itsshare trading volume divided by its total shares outstanding.
• One-month abnormal turnover. A firm’s abnormal turnover is calculated as theratio of its average daily turnover over the past 20 days to its average dailyturnover over the past 250 days.
9. Reversal. The sorting measure used is the stock’s one-month return, computed as thecumulative return over the past 20 trading days.
For every anomaly except one-month return reversal, we sort the stock universe eachmonth using the most recent month-end measures and then hold the resulting portfolios forone month. Because one-month return reversal is a short-term anomaly, we sort the stockuniverse each day based on the most recently available 20-day cumulative return. Using thissort, we rebalance a one-fifth “slice” of the total portfolio that is then held for five tradingdays. Each day we average the returns across the five slices. Those resulting daily returnsare then compounded across days to compute the reversal anomaly’s monthly return. For allanomalies, value-weighted portfolios of stocks within the top and bottom deciles are formedusing the most recent month-end market capitalizations as weights.
A.3. The IPO review process in China
The process of IPO review by the CSRC involves seven steps:
1. Confirmation of application receipt. The reception department in the bureau organizesall of the application packages, confirms with each applicant firm the receipt of all materials,and makes the offering proposals public.
39
2. Application material pre-check (feedback provided). In this step, the offering administra-tion department assigns a team to pre-check all application materials and prepare a writtenreport indicating whether more material/information is needed and suggesting the potentialconcerns or issues with the offering for further reviews. After receiving the written report,the applicant firm can work with investment bankers to revise the application package.
3. Communication meeting. The applicant’s IPO team meets with the offering administra-tion department, but no material issues are discussed.
4. Update disclosed offering proposal. After revising the application package and uponreceiving the offering administration team’s approval, the applicant’s team can revise theinitially disclosed offering proposal.
5. Initial review meeting. An offering committee team and the offering administrativedepartment attend the meeting to review thoroughly whether the applicant firm’s currentcondition and growth prospects satisfy IPO criteria.
6. Final offering review meeting. A different offering committee team votes on whether ornot to approve the firm’s IPO application based on the results of the initial review meetingdiscussion.
7. Offering. The applicant firm may still need to revise its application package based onthe decision in the Final Offering Review Meeting. Following that, the firm can prepare theoffering.
A.4. Reverse-merger data and shell-value estimation
Our reverse merger data are from WIND and cover the 2007 to 2016 period. In July 2007,the CSRC issued a ruling that formed a special committee in its Public Offering Departmentto strengthen the review process for M&A applications. Subsequently, the CSRC took a moreactive role in the M&A review process, increasing reporting transparency and quality. Inthe same ruling, the CSRC identified several characteristics of M&A cases that classify themas reverse mergers, to be handled with more scrutiny. The improved reporting transparencyand CSRC’s specification of reverse mergers made it possible to trace reverse-merger cases.
To construct the daily series of estimated shell values, we first estimate p and G inequation (1) as follows:
1. Probability of becoming a shell (p). Each day, we calculate the fraction of stocks,among those in the bottom 30%, involved in reverse merger deals during the past 730calendar days. We use that fraction as the empirical probability estimate of becominga shell within in a two-year window, converting the value to a one-year probability(essentilly by halving it).
2. Value appreciation upon becoming a shell (G). For each reverse merger case amongthe bottom 30%, the value appreciation equals the change in market value over a time
40
window beginning 60 days before the board’s announcement of a proposed deal proposaland ending 60 days after the deal’s CSRC approval. On each day, the estimated valueof G is the average value appreciation in all reverse-merger deals whose windows endduring the past 730 calendar days.
A.5. Return variation related to shell value
Here we investigate the sensitivity of the returns on the smallest stocks to two variablesthat proxy for fluctuations in shell values. The first variable reflects variation in the reverse-merger premium. For each reverse-merger event, we define an event window beginning 60days before the shell firm’s board meeting announcing the proposal and ending 60 days afterCSRC approval. Each day we compute the average return of all stocks that are within theirevent window, and then we compound those daily average returns to form a reverse-mergerreturn for month t, RMt. We associate a relatively high value of RMt with an increase inshell value during that month. Our hypothesis is that returns on stocks in the bottom 30% ofthe size distribution are more sensitive to RMt than are other stocks. For each of three sizegroups, formed by dividing the universe of all listed stocks at the 30th and 70th percentiles,we estimate the regression,
Rt = a+ bRMt + γFt + εt (3)
where Rt is the size group’s value-weighted monthly return, and the vector Ft contains theother two size groups’ returns. For example, when the regression has the return on thesmallest stocks on the left-hand side, Ft includes the returns on the middle- and large-capgroups. We expect b to be positive for the smallest stocks but not for the other two sizegroups. Panel A of Table A2 reports the regression results. We see that indeed the estimateof b is significantly positive for the smallest stocks but is negative for the other two sizegroups.
The second proxy for capturing fluctuations in shell value is the log of the total numberof IPOs in month t, with the rationale that a greater frequency of IPOs could be interpretedby the market as a relaxing of IPO constraints and thus a reduction in reverse-merger shellvalue. Under our shell-value hypothesis, we expect stock returns to covary negatively withIPO numbers for the smallest stocks but not for the other two size groups. The regression isthe same as regression (3) except that RMt is replaced by the log IPO number, log(NIPOt).Panel B of Table A2 reports the results. Consistent with our hypothesis, the estimate of bis negative for the smallest stocks, although the t-statistic of −1.53 falls somewhat short ofsignificance. In contrast, the estimate of b is insignificant and positive (t-statistic: 1.18) forthe middle group, while it has a t-statistic of just −0.50 for the large-cap group.
The results from both sets of regressions are consistent our hypothesis that the returnson stocks in the bottom 30% reflect, in substantial part, variation in the value of being apotential reverse-merger shell. In other words, the values of these “small” stocks reflect morethan the businesses of the underlying small firms.
41
A.6. Excluding financial firms from Table 2
Table A3 reports the results of re-computing the same regressions reported in Table 2but with financial firms excluded. On average the financial firms include 79 real estate firmsand 20 other firms in banking and financial services. The results in Table A3 are very similarto those in Table 2.
A.7. Additional model-comparison results
Table A4 reports details of the regressions underlying the results reported in Table 5.Each model’s size factor loads strongly on the other model’s size factor, producing t-statisticsof about 39 in each case. The models’ value factors also load significantly on each other, butless strongly, with t-statistics of 2.83 and 3.49. The size factor of FF-3 loads significantlynegatively on the value factor of CH-3, with a t-statistic of −8.3, but CH-3’s size factor doesnot load significantly on FF-3’s value factor. Similarly, CH-3’s value factor loads significantlynegatively on FF-3’s size factor (t-statistic: −11.15), but not vice versa.
Model CH-3 dominates FF-3 not only in the frequentist comparisons reported in Table 5but also in a Bayesian comparison that follows the Stambaugh and Yuan (2017) procedurein applying the analysis of Barillas and Shanken (2018). Suppose we compare two models,M1 and M2, and before observing the data we assign probabilities p(M1) and p(M2) to eachmodel being the right one, with p(M1) + p(M2) = 1 . After observing the data, D, theposterior probability of model i is given by
p(Mi|D) =p(Mi) · p(D|Mi)
p(M1) · p(D|M1) + p(M2) · p(D|M2), (4)
where model i’s marginal likelihood is given by
p(D|Mi) =
∫θi
p(θi)p(D|θi)dθi, (5)
where p(θi) is the prior distribution for model i’s parameters, and p(D|θi) is the likelihoodfunction for model i. As shown by Barillas and Shanken (2018), whenD includes observationsof the factors in both models (including the market) as well as a common set of “test” assets,the latter drop out of the computation in Equation (4). Moreover, that study also showsthat when p(θi) follows a form as in Pastor and Stambaugh (2000), then p(D|Mi) can becomputed analytically. The key feature of the prior, p(θi), is that it is informative abouthow large a Sharpe ratio can be produced by combining a given set of assets, in this casethe assets represented by the model’s factors. Specifically, the prior implies a value forthe expected maximum squared Sharpe ratio, relative to the (observed) Sharpe ratio of themarket. We use the Barillas and Shanken (2018) analytical results here to compute posteriormodel probabilities in the above two-way model comparison. Prior model probabilities ofeach model are set to one-half.
42
Fig. A.1 displays posterior model probabilities in the comparison of CH-3 to FF-3. Thevalue on the horizontal axis is the square root of the prior expected maximum squaredSharpe ratio achievable by combining the model’s factors, [Eprior{S2
MAX}]1/2, divided bythe observed Sharpe ratio of the market, SMKT . We see that the data strongly favor CH-3over FF-3. In fact, the posterior probability of CH-3 essentially equals one if the Sharpe-ratiomultiplier on the horizontal axis exceeds only 1.05 or so, corresponding to a prior expectationthat the market’s Sharpe ratio can be improved only very modestly.
We also find that CH-3 dominates the frequentist comparisons reported in Table 5 whenFF-3 is replaced by FF-5, the replication in China of the five-factor model in Fama andFrench (2015). Table A5 reports those results. As with FF-3, FF-5 fails to explain eitherSMB or VMG from model CH-3, leaving those factors’ FF-5 alphas with t-statistics of 2.41and 4.39 and producing a GRS p-value of just 0.0003. In contrast, the CH-3 alphas for thefour non-market factors in FF-5 are all insignificant, having t-statistics of 0.87 or less inmagnitude and producing a large GRS p-value of 0.88.
43
Table A1Chinese anomalies in the literature
The table provides a compilation of the anomalies reported by one or more studies as being significant inChina. The studies analyzing each anomaly are listed, including those reporting an anomaly to be insignificant(identified as such in the table). For each anomaly variable, we also report CAPM alphas for both unconditionaland conditional sorts. For the unconditional sorts, the long leg of an anomaly is the value-weighted portfolio ofstocks in the lowest decile of the anomaly measure, and the short leg contains the stocks in the highest decile,where a high value of the measure is associated with lower return. For the conditional sorts, long/short legs areneutralized with respect to size. That is, we first form size deciles by sorting on the previous month’s marketvalue. Within each size decile, we then create ten deciles formed by sorting on the anomaly variable. Finally,we form the anomaly’s decile portfolios, with each portfolio pooling the stocks in a given anomaly decile acrossthe size groups, again with value weighting. Our sample period is January 2000 through December 2016 (204months). All t-statistics (in parentheses) are based on the heteroscedasticity-consistent standard errors ofWhite (1980).
CAPM alpha (monthly %)Category Anomaly References Unconditional Size-neutral
Size Market Cap Wang and Xu (2004), Eun and Huang (2007),Cheung et al. (2015), Cakici, Chan, andTopyan (2015), Hsu, Viswanathan, Wang, andWool (2017), Carpenter, Lu, and Whitelaw(2017), and Hu et al. (2018). Reported in-significant: Chen et al. (2010) and Cheunget al. (2015).
0.97(1.81)
—
Value EP Cakici et al. (2015) and Hsu et al. (2017). Re-ported insignificant: Chen et al. (2010) andHu et al. (2018).
1.37(2.93)
1.89(4.72)
Value BM Wang and Xu (2004), Eun and Huang (2007),Chen et al. (2010), Cheung et al. (2015), Ca-kici et al. (2015), Hsu et al. (2017), and Car-penter et al. (2017). Reported insignificant:Hu et al. (2018).
1.14(2.13)
1.10(2.22)
Value CP Cakici et al. (2015). Reported insignificant:Wang and Di Iorio (2007) and Chen et al.(2010).
0.70(1.69)
0.76(2.25)
Profitability ROE Guo et al. (2017). Reported insignificant: Li,Yao, and Pu (2007).
0.93(2.11)
1.50(4.11)
Volatility 1-Mo. Vol. Cheung et al. (2015), Cakici et al. (2015),and Hsu et al. (2017). Reported insignificant:Chen et al. (2010).
1.03(2.31)
0.90(2.19)
Volatility MAX Carpenter et al. (2017). 0.81(2.02)
0.60(1.61)
44
Table A1Chinese anomalies in the literature (continued)
CAPM alpha (monthly %)Category Anomaly References Unconditional Size-neutral
Reversal 1-Month Return Cakici et al. (2015), Hsu et al. (2017), andCarpenter et al. (2017). Reported insignifi-cant: Cheung et al. (2015).
1.49(3.06)
1.65(3.68)
Turnover 12-Mo. Turn. Zhang and Liu (2006) and Eun and Huang(2007). Reported insignificant: Chen et al.(2010).
0.53(1.09)
0.74(1.74)
Turnover 1-Mo. Abn. Turn. Li (2004) and Zhang and Liu (2006). 1.27(2.92)
1.39(3.68)
Investment Asset Growth Chen et al. (2010). Reported insignificant:Hsu et al. (2017), Guo et al. (2017), and Lin(2017).
0.22(0.72)
−0.05(−0.20)
Accruals Accruals Li, Niu, Zhang, and Largay (2011) and Hsuet al. (2017). Reported insignificant: Chenet al. (2010).
0.08(0.39)
−0.15(−0.70)
Accruals NOA Chen et al. (2010) and Hsu et al. (2017). 0.38(1.03)
0.42(1.22)
Illiquidity Amihud-Illiq. Carpenter et al. (2017) and Chen et al. (2010). 0.83(1.62)
0.63(1.55)
45
Table A2Sensitivities of size-group returns to proxies for fluctuations in shell values
For each of three size groups, formed by dividing the universe of all listed stocks at the 30th and 70thpercentiles, the table reports the estimate of b in the regression,
Rt = a+ bShellt + γFt + εt,
where Rt is the value-weighted return for the size group, Shell is a proxy for fluctuations in the value ofpotentially becoming a reverse-merger shell, and the vector Ft contains the returns on the other two sizegroups. In Panel A, Shellt is the average return of shell stocks experiencing reverse mergers, RMt. In PanelB, Shellt is the log number of IPOs, log(NIPOt). The sample period is January 2007 through December2016. All t-statistics (in parentheses) are based on the heteroscedasticity-consistent standard errors of White(1980).
Smallest LargestStocks Middle Stocks
Panel A. Shellt = RMt
0.963 −1.267 −0.330(2.19) (−3.02) (−4.65)
Panel B. Shellt = log(NIPOt)
−0.023 0.013 −0.001(−1.53) (1.18) (−0.50)
46
Table
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Qu
anti
ty(1
)(2
)(3
)(4
)(5
)(6
)(7
)(8
)(9
)
Inte
rcep
t0.
0134
0.0
646
0.06
100.
0693
0.06
420.
0714
0.0
602
0.0
722
0.0
750
(1.7
8)
(3.6
9)(3
.40)
(4.0
8)(3
.79)
(4.1
6)(3
.39)
(4.4
1)
(4.5
1)
β0.0
010
0.00
03−
0.00
06−
0.00
040.
0014
0.0
002
0.0
007
0.0
008
(0.3
4)
(0.0
9)(−
0.23
)(−
0.17
)(0
.49)
(0.0
9)(0
.26)
(0.3
1)
logME
−0.
0056
−0.
0052
−0.
0051
−0.
0051
−0.
0072
−0.0
053
−0.
006
8−
0.0
069
(−3.
37)
(−3.
04)
(−3.
07)
(−3.
14)
(−4.
64)
(−3.0
9)
(−4.
48)
(−4.4
4)
logBM
0.00
530.
001
70.
003
2
(2.7
9)(0
.96)
(1.7
6)
logAM
0.00
410.
001
5
(2.5
5)(0
.94)
EP
+1.
0123
0.8
555
0.8
572
(4.7
8)(4
.51)
(4.5
1)
D(EP<
0)
0.00
01−
0.0
012
−0.
000
7
(0.0
3)(−
0.6
8)
(−0.
36)
CP
+0.0
391
0.0
122
(2.2
6)(0
.79)
D(CP<
0)0.0
009
0.0
009
(1.3
1)(1
.20)
R2
0.0
193
0.02
640.
0429
0.06
430.
0660
0.06
150.
043
40.
082
50.0
776
47
Table A4Regressions of CH-3 and FF-3 size and value factors on the other model’s factors
Each row reports a factor’s mean, its estimated monthly alpha (in percent), and the factor’s loadings with respectto the other model. White (1980) heteroscedasticity-consistent t-statistics are in parentheses. The sample is from2000 to 2016.
Factors
Dep. variable Mean (%) Alpha (%) MKT SMB VMG FFSMB FFHML
FFSMB 0.64 −0.04 −0.01 0.95 −0.25
(1.84) (−0.66) (−0.69) (38.79) (−8.33)
FFHML 0.84 0.34 0.05 −0.00 0.41
(2.60) (0.97) (0.96) (−0.04) (2.83)
SMB 1.03 0.47 −0.01 0.89 0.00
(3.26) (7.03) (−1.24) (39.28) (0.07)
VMG 1.14 1.39 −0.08 −0.50 0.14
(4.35) (7.93) (−3.15) (−11.15) (3.49)
48
Table A5Abilities of models CH-3 and FF-5 to explain each other’s factors
Panel A reports a factor’s estimated monthly alpha (in percent) with respect to the other model (withWhite, 1980, heteroscedasticity-consistent t-statistics in parentheses). Panel B computes the Gibbons-Ross-Shanken(1989) F -test of whether a given model produces zero alphas for the factors of the other model (p-valuein parentheses). The sample period is January 2000 through December 2016.
Alphas with respect to:
Factors CH-3 FF-5
Panel A: Alpha (t-statatistics)
SMB - 0.14
- (2.41)
VMG - 0.43
- (4.39)
FFSMB 0.01 -
(0.18) -
FFHML 0.34 -
(0.96) -
FFRMW −0.10 -
(−0.86) -
FFCMA −0.08 -
(−0.51) -
Panel B: GRS F -statistics (p-value)
SMB, VMG - 8.43
- (0.0003)
FFSMB, FFHML, 0.29 -
FFRMW , FFCMA (0.88) -
49
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
FF-3CH-3
Fig. A.1. Model probabilities comparing model CH-3 to model FF-3. The figure displays Bayesianposterior model probabilities for the two-way model comparison. The value on the horizontal axisis the square root of the prior expected maximum Sharpe ratio achievable by combining the model’sfactors, divided by the observed Sharpe ratio of the market. Prior model probabilities are equal.The sample period is from January 2000 through December 2016 (204 months)
50
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